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bettermarks »Math glossary» Gauß, Carl Friedrich

Surname: Carl Friedrich Gauss

Born: 1777 in Braunschweig

Died: 1855 in Göttingen

Teaching / research areas: Astronomy, statistics, algebra, geometry, number theory, physics, geodesy

Carl Friedrich Gauß was an important German mathematician and scientist who lived in the 18th and 19th centuries. He is considered a "child prodigy" and made important achievements in various areas of mathematics, physics, astronomy and geodesy. Perhaps best known are those Gaussian bell curve and the Least Squares Method, by means of which Gauss succeeded in the sensational rediscovery of a dwarf planet. He contributed to algebra the first complete proof of its fundamental theorem; he expanded geometry to include differential geometry and non-Euclidean geometry; in the field of number theory, among other things, he recognized the relationship between prime numbers and logarithms. Gauss achieved great fame during his lifetime, although he did not publish a large number of his research results.

Life

Carl Friedrich Gauß was born in Braunschweig in 1777 as the second son of a poor family. As a Gaussian, his extraordinary math skills were already evident at the age of nine Gaussian empirical formula discovered. When Gauss was 14 years old, the Duke of Braunschweig was enthusiastic about his skills and supported him financially. Gauß was able to study at the Collegium Carolinum for three years before moving to the University of Göttingen in 1795. Here, a year later, he was the first to succeed in proving the constructability of the regular seventeenth-corner. Only after this sensational success did he give up the plan to study philology in favor of mathematics. After receiving his doctorate, he researched and published with the support of the Duke of Braunschweig Disquisitiones Arithmeticae, in which he summarized and systematically developed number theory. After the Duke's death, Gauss became professor and director of the Göttingen observatory. There he died at the age of 78.

The person Gauss

Gauss was religious, conservative and monarchist. In his private life he had to get over the deaths of his two wives and his daughter. During his lifetime he achieved great fame for his scientific achievements, although he had never published many of his discoveries. It was only with the discovery of his diary in 1898 that posterity understood the significance and scope of his discoveries. On a commemorative coin from 1856 he is called the "Prince of Mathematicians" (Mathematicorum Principi) designated. A series of 10 DM notes showed a portrait of Gauss and a picture of the Gaussian bell curve.

The diversity and depth of Gauß's scientific achievements do not allow all of them to be mentioned at this point. A few should be named as representative.

The Gaussian bell curve and the least squares method

Perhaps best known is that Gaussian bell curve, the probability density function of the normal distribution that Gauss used for his astronomical calculations. He developed, independently of the French mathematician Legendre, the standard mathematical method of equalization calculation, the Least Squares Method. With these he succeeded in the sensational recovery of the dwarf planet Ceres.

Contributions to analysis and algebra

Gauss succeeded in the first complete proof of the Fundamental theorem of algebra, according to which every algebraic equation has at least one solution (or, in other words, the field \ (mathbb C \) of the complex numbers is algebraically closed). He developed this to solve systems of linear equations Gaussian elimination method. He discovered various methods of numerical computation of integrals known as Gaussian quadrature. As Gaussian integral theorem one denotes a result from the vector analysis. The geometric representation of the set of complex numbers is made according to him Gaussian plane of numbers called.

Contributions to number theory

In the field of number theory, he recognized, among other things, the connection between the distribution of prime numbers and the growth of the logarithmic function. The quadratic reciprocity law he proved not in one way, but in several ways throughout his life. To calculate the decimal places of the circle number Pi, he developed the Gauss – Legendre algorithm (Legendre discovered him independently of him).

New geometries

As for geometry, Gauss anticipated non-Euclidean geometries (but did not publish this result) and developed the fundamentals of differential geometry, which links geometry to analysis. He led the Gaussian curvature one and be proven Theorema egregium (such as "excellent theorem"), which relates the sum of angles in triangles to the curvature.

Gauss also made important contributions to geodesy, optics and magnetism.

Image source: Wikipedia